I need to simulate the following (double indexed!) recurrence relation:

p[1,1]=1

for n=1,2,3,… and k=1,2,…,n+1

p[n+1,k] = p[n,k]*(1-v*k/n) + p[n,k-1]*v*(k-1)/n , with p[n,0]=p[n,n+1]=0

where v is just some constant in the interval (0,1)

For a fixed value of n, say n=20, I need to compute p[n,k] for k=1,2,…,n

Thanks, Dave

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